What is the Sharpe ratio, Treynor ratio, and Jensen’s alpha for each portfolio?

Question

What is the Sharpe ratio, Treynor ratio, and Jensen’s alpha for each portfolio? (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your Sharpe ratio answers and Treynor ratio answers to 5 decimal places and Jensen's alpha answers to 2 decimal places. Omit the "%" sign in your response.)

Consider the following information concerning three portfolios, the market portfolio, and the risk-free asset:

Explanation / Answer

Calculate the Sharpe ratio, treynor ratio and Jensen’s alpha for each portfolio:

Sharpe ratio:

= (rp - rf) / p

For Stock X:

= (11.5 – 4.6) / 38

= 0.1816

For Stock Y:

= (10.5 – 4.6) / 33

= 0.17879

For Stock Z:

= (7.2 – 4.6) / 23

= 0.11304

Treynor ratio:

= (Rp - Rf) / Beta

For Stock X:

= (11.5 – 4.6) / 1.70

= 4.059

For Stock Y:

= (10.5 – 4.6) /1.30

= 4.5385

For Stock Z:

= (7.2 – 4.6) / 0.85

= 3.059

Jensen’s alpha:

= Rp – [Rf + * (Rm - Rf)

For Stock X:

= 11.5 – [4.6 + 1.7 *(10.9 – 4.6)]

= -3.81

For Stock Y:

= 10.5 – [4.6 + 1.3 * (10.9 -4.6)]

= -2.29

For Stock Z:

= 7.2 – [4.6 + 0.85 * (10.9-4.6)]

= - 2.755

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